use core::mem; use core::num::FpCategory; use core::ops::{Add, Div, Neg}; use core::f32; use core::f64; use {Num, NumCast, ToPrimitive}; #[cfg(all(not(feature = "std"), feature = "libm"))] use libm; /// Generic trait for floating point numbers that works with `no_std`. /// /// This trait implements a subset of the `Float` trait. pub trait FloatCore: Num + NumCast + Neg + PartialOrd + Copy { /// Returns positive infinity. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T) { /// assert!(T::infinity() == x); /// } /// /// check(f32::INFINITY); /// check(f64::INFINITY); /// ``` fn infinity() -> Self; /// Returns negative infinity. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T) { /// assert!(T::neg_infinity() == x); /// } /// /// check(f32::NEG_INFINITY); /// check(f64::NEG_INFINITY); /// ``` fn neg_infinity() -> Self; /// Returns NaN. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// /// fn check() { /// let n = T::nan(); /// assert!(n != n); /// } /// /// check::(); /// check::(); /// ``` fn nan() -> Self; /// Returns `-0.0`. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(n: T) { /// let z = T::neg_zero(); /// assert!(z.is_zero()); /// assert!(T::one() / z == n); /// } /// /// check(f32::NEG_INFINITY); /// check(f64::NEG_INFINITY); /// ``` fn neg_zero() -> Self; /// Returns the smallest finite value that this type can represent. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T) { /// assert!(T::min_value() == x); /// } /// /// check(f32::MIN); /// check(f64::MIN); /// ``` fn min_value() -> Self; /// Returns the smallest positive, normalized value that this type can represent. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T) { /// assert!(T::min_positive_value() == x); /// } /// /// check(f32::MIN_POSITIVE); /// check(f64::MIN_POSITIVE); /// ``` fn min_positive_value() -> Self; /// Returns epsilon, a small positive value. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T) { /// assert!(T::epsilon() == x); /// } /// /// check(f32::EPSILON); /// check(f64::EPSILON); /// ``` fn epsilon() -> Self; /// Returns the largest finite value that this type can represent. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T) { /// assert!(T::max_value() == x); /// } /// /// check(f32::MAX); /// check(f64::MAX); /// ``` fn max_value() -> Self; /// Returns `true` if the number is NaN. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, p: bool) { /// assert!(x.is_nan() == p); /// } /// /// check(f32::NAN, true); /// check(f32::INFINITY, false); /// check(f64::NAN, true); /// check(0.0f64, false); /// ``` #[inline] fn is_nan(self) -> bool { self != self } /// Returns `true` if the number is infinite. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, p: bool) { /// assert!(x.is_infinite() == p); /// } /// /// check(f32::INFINITY, true); /// check(f32::NEG_INFINITY, true); /// check(f32::NAN, false); /// check(f64::INFINITY, true); /// check(f64::NEG_INFINITY, true); /// check(0.0f64, false); /// ``` #[inline] fn is_infinite(self) -> bool { self == Self::infinity() || self == Self::neg_infinity() } /// Returns `true` if the number is neither infinite or NaN. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, p: bool) { /// assert!(x.is_finite() == p); /// } /// /// check(f32::INFINITY, false); /// check(f32::MAX, true); /// check(f64::NEG_INFINITY, false); /// check(f64::MIN_POSITIVE, true); /// check(f64::NAN, false); /// ``` #[inline] fn is_finite(self) -> bool { !(self.is_nan() || self.is_infinite()) } /// Returns `true` if the number is neither zero, infinite, subnormal or NaN. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, p: bool) { /// assert!(x.is_normal() == p); /// } /// /// check(f32::INFINITY, false); /// check(f32::MAX, true); /// check(f64::NEG_INFINITY, false); /// check(f64::MIN_POSITIVE, true); /// check(0.0f64, false); /// ``` #[inline] fn is_normal(self) -> bool { self.classify() == FpCategory::Normal } /// Returns the floating point category of the number. If only one property /// is going to be tested, it is generally faster to use the specific /// predicate instead. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// use std::num::FpCategory; /// /// fn check(x: T, c: FpCategory) { /// assert!(x.classify() == c); /// } /// /// check(f32::INFINITY, FpCategory::Infinite); /// check(f32::MAX, FpCategory::Normal); /// check(f64::NAN, FpCategory::Nan); /// check(f64::MIN_POSITIVE, FpCategory::Normal); /// check(f64::MIN_POSITIVE / 2.0, FpCategory::Subnormal); /// check(0.0f64, FpCategory::Zero); /// ``` fn classify(self) -> FpCategory; /// Returns the largest integer less than or equal to a number. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, y: T) { /// assert!(x.floor() == y); /// } /// /// check(f32::INFINITY, f32::INFINITY); /// check(0.9f32, 0.0); /// check(1.0f32, 1.0); /// check(1.1f32, 1.0); /// check(-0.0f64, 0.0); /// check(-0.9f64, -1.0); /// check(-1.0f64, -1.0); /// check(-1.1f64, -2.0); /// check(f64::MIN, f64::MIN); /// ``` #[inline] fn floor(self) -> Self { let f = self.fract(); if f.is_nan() || f.is_zero() { self } else if self < Self::zero() { self - f - Self::one() } else { self - f } } /// Returns the smallest integer greater than or equal to a number. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, y: T) { /// assert!(x.ceil() == y); /// } /// /// check(f32::INFINITY, f32::INFINITY); /// check(0.9f32, 1.0); /// check(1.0f32, 1.0); /// check(1.1f32, 2.0); /// check(-0.0f64, 0.0); /// check(-0.9f64, -0.0); /// check(-1.0f64, -1.0); /// check(-1.1f64, -1.0); /// check(f64::MIN, f64::MIN); /// ``` #[inline] fn ceil(self) -> Self { let f = self.fract(); if f.is_nan() || f.is_zero() { self } else if self > Self::zero() { self - f + Self::one() } else { self - f } } /// Returns the nearest integer to a number. Round half-way cases away from `0.0`. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, y: T) { /// assert!(x.round() == y); /// } /// /// check(f32::INFINITY, f32::INFINITY); /// check(0.4f32, 0.0); /// check(0.5f32, 1.0); /// check(0.6f32, 1.0); /// check(-0.4f64, 0.0); /// check(-0.5f64, -1.0); /// check(-0.6f64, -1.0); /// check(f64::MIN, f64::MIN); /// ``` #[inline] fn round(self) -> Self { let one = Self::one(); let h = Self::from(0.5).expect("Unable to cast from 0.5"); let f = self.fract(); if f.is_nan() || f.is_zero() { self } else if self > Self::zero() { if f < h { self - f } else { self - f + one } } else { if -f < h { self - f } else { self - f - one } } } /// Return the integer part of a number. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, y: T) { /// assert!(x.trunc() == y); /// } /// /// check(f32::INFINITY, f32::INFINITY); /// check(0.9f32, 0.0); /// check(1.0f32, 1.0); /// check(1.1f32, 1.0); /// check(-0.0f64, 0.0); /// check(-0.9f64, -0.0); /// check(-1.0f64, -1.0); /// check(-1.1f64, -1.0); /// check(f64::MIN, f64::MIN); /// ``` #[inline] fn trunc(self) -> Self { let f = self.fract(); if f.is_nan() { self } else { self - f } } /// Returns the fractional part of a number. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, y: T) { /// assert!(x.fract() == y); /// } /// /// check(f32::MAX, 0.0); /// check(0.75f32, 0.75); /// check(1.0f32, 0.0); /// check(1.25f32, 0.25); /// check(-0.0f64, 0.0); /// check(-0.75f64, -0.75); /// check(-1.0f64, 0.0); /// check(-1.25f64, -0.25); /// check(f64::MIN, 0.0); /// ``` #[inline] fn fract(self) -> Self { if self.is_zero() { Self::zero() } else { self % Self::one() } } /// Computes the absolute value of `self`. Returns `FloatCore::nan()` if the /// number is `FloatCore::nan()`. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, y: T) { /// assert!(x.abs() == y); /// } /// /// check(f32::INFINITY, f32::INFINITY); /// check(1.0f32, 1.0); /// check(0.0f64, 0.0); /// check(-0.0f64, 0.0); /// check(-1.0f64, 1.0); /// check(f64::MIN, f64::MAX); /// ``` #[inline] fn abs(self) -> Self { if self.is_sign_positive() { return self; } if self.is_sign_negative() { return -self; } Self::nan() } /// Returns a number that represents the sign of `self`. /// /// - `1.0` if the number is positive, `+0.0` or `FloatCore::infinity()` /// - `-1.0` if the number is negative, `-0.0` or `FloatCore::neg_infinity()` /// - `FloatCore::nan()` if the number is `FloatCore::nan()` /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, y: T) { /// assert!(x.signum() == y); /// } /// /// check(f32::INFINITY, 1.0); /// check(3.0f32, 1.0); /// check(0.0f32, 1.0); /// check(-0.0f64, -1.0); /// check(-3.0f64, -1.0); /// check(f64::MIN, -1.0); /// ``` #[inline] fn signum(self) -> Self { if self.is_nan() { Self::nan() } else if self.is_sign_negative() { -Self::one() } else { Self::one() } } /// Returns `true` if `self` is positive, including `+0.0` and /// `FloatCore::infinity()`, and since Rust 1.20 also /// `FloatCore::nan()`. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, p: bool) { /// assert!(x.is_sign_positive() == p); /// } /// /// check(f32::INFINITY, true); /// check(f32::MAX, true); /// check(0.0f32, true); /// check(-0.0f64, false); /// check(f64::NEG_INFINITY, false); /// check(f64::MIN_POSITIVE, true); /// check(-f64::NAN, false); /// ``` #[inline] fn is_sign_positive(self) -> bool { !self.is_sign_negative() } /// Returns `true` if `self` is negative, including `-0.0` and /// `FloatCore::neg_infinity()`, and since Rust 1.20 also /// `-FloatCore::nan()`. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, p: bool) { /// assert!(x.is_sign_negative() == p); /// } /// /// check(f32::INFINITY, false); /// check(f32::MAX, false); /// check(0.0f32, false); /// check(-0.0f64, true); /// check(f64::NEG_INFINITY, true); /// check(f64::MIN_POSITIVE, false); /// check(f64::NAN, false); /// ``` #[inline] fn is_sign_negative(self) -> bool { let (_, _, sign) = self.integer_decode(); sign < 0 } /// Returns the minimum of the two numbers. /// /// If one of the arguments is NaN, then the other argument is returned. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, y: T, min: T) { /// assert!(x.min(y) == min); /// } /// /// check(1.0f32, 2.0, 1.0); /// check(f32::NAN, 2.0, 2.0); /// check(1.0f64, -2.0, -2.0); /// check(1.0f64, f64::NAN, 1.0); /// ``` #[inline] fn min(self, other: Self) -> Self { if self.is_nan() { return other; } if other.is_nan() { return self; } if self < other { self } else { other } } /// Returns the maximum of the two numbers. /// /// If one of the arguments is NaN, then the other argument is returned. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, y: T, max: T) { /// assert!(x.max(y) == max); /// } /// /// check(1.0f32, 2.0, 2.0); /// check(1.0f32, f32::NAN, 1.0); /// check(-1.0f64, 2.0, 2.0); /// check(-1.0f64, f64::NAN, -1.0); /// ``` #[inline] fn max(self, other: Self) -> Self { if self.is_nan() { return other; } if other.is_nan() { return self; } if self > other { self } else { other } } /// Returns the reciprocal (multiplicative inverse) of the number. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, y: T) { /// assert!(x.recip() == y); /// assert!(y.recip() == x); /// } /// /// check(f32::INFINITY, 0.0); /// check(2.0f32, 0.5); /// check(-0.25f64, -4.0); /// check(-0.0f64, f64::NEG_INFINITY); /// ``` #[inline] fn recip(self) -> Self { Self::one() / self } /// Raise a number to an integer power. /// /// Using this function is generally faster than using `powf` /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// /// fn check(x: T, exp: i32, powi: T) { /// assert!(x.powi(exp) == powi); /// } /// /// check(9.0f32, 2, 81.0); /// check(1.0f32, -2, 1.0); /// check(10.0f64, 20, 1e20); /// check(4.0f64, -2, 0.0625); /// check(-1.0f64, std::i32::MIN, 1.0); /// ``` #[inline] fn powi(mut self, mut exp: i32) -> Self { if exp < 0 { exp = exp.wrapping_neg(); self = self.recip(); } // It should always be possible to convert a positive `i32` to a `usize`. // Note, `i32::MIN` will wrap and still be negative, so we need to convert // to `u32` without sign-extension before growing to `usize`. super::pow(self, (exp as u32).to_usize().unwrap()) } /// Converts to degrees, assuming the number is in radians. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(rad: T, deg: T) { /// assert!(rad.to_degrees() == deg); /// } /// /// check(0.0f32, 0.0); /// check(f32::consts::PI, 180.0); /// check(f64::consts::FRAC_PI_4, 45.0); /// check(f64::INFINITY, f64::INFINITY); /// ``` fn to_degrees(self) -> Self; /// Converts to radians, assuming the number is in degrees. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(deg: T, rad: T) { /// assert!(deg.to_radians() == rad); /// } /// /// check(0.0f32, 0.0); /// check(180.0, f32::consts::PI); /// check(45.0, f64::consts::FRAC_PI_4); /// check(f64::INFINITY, f64::INFINITY); /// ``` fn to_radians(self) -> Self; /// Returns the mantissa, base 2 exponent, and sign as integers, respectively. /// The original number can be recovered by `sign * mantissa * 2 ^ exponent`. /// /// # Examples /// /// ``` /// use num_traits::float::FloatCore; /// use std::{f32, f64}; /// /// fn check(x: T, m: u64, e: i16, s:i8) { /// let (mantissa, exponent, sign) = x.integer_decode(); /// assert_eq!(mantissa, m); /// assert_eq!(exponent, e); /// assert_eq!(sign, s); /// } /// /// check(2.0f32, 1 << 23, -22, 1); /// check(-2.0f32, 1 << 23, -22, -1); /// check(f32::INFINITY, 1 << 23, 105, 1); /// check(f64::NEG_INFINITY, 1 << 52, 972, -1); /// ``` fn integer_decode(self) -> (u64, i16, i8); } impl FloatCore for f32 { constant! { infinity() -> f32::INFINITY; neg_infinity() -> f32::NEG_INFINITY; nan() -> f32::NAN; neg_zero() -> -0.0; min_value() -> f32::MIN; min_positive_value() -> f32::MIN_POSITIVE; epsilon() -> f32::EPSILON; max_value() -> f32::MAX; } #[inline] fn integer_decode(self) -> (u64, i16, i8) { integer_decode_f32(self) } #[inline] #[cfg(not(feature = "std"))] fn classify(self) -> FpCategory { const EXP_MASK: u32 = 0x7f800000; const MAN_MASK: u32 = 0x007fffff; // Safety: this identical to the implementation of f32::to_bits(), // which is only available starting at Rust 1.20 let bits: u32 = unsafe { mem::transmute(self) }; match (bits & MAN_MASK, bits & EXP_MASK) { (0, 0) => FpCategory::Zero, (_, 0) => FpCategory::Subnormal, (0, EXP_MASK) => FpCategory::Infinite, (_, EXP_MASK) => FpCategory::Nan, _ => FpCategory::Normal, } } #[inline] #[cfg(not(feature = "std"))] fn to_degrees(self) -> Self { // Use a constant for better precision. const PIS_IN_180: f32 = 57.2957795130823208767981548141051703_f32; self * PIS_IN_180 } #[inline] #[cfg(not(feature = "std"))] fn to_radians(self) -> Self { self * (f32::consts::PI / 180.0) } #[cfg(feature = "std")] forward! { Self::is_nan(self) -> bool; Self::is_infinite(self) -> bool; Self::is_finite(self) -> bool; Self::is_normal(self) -> bool; Self::classify(self) -> FpCategory; Self::floor(self) -> Self; Self::ceil(self) -> Self; Self::round(self) -> Self; Self::trunc(self) -> Self; Self::fract(self) -> Self; Self::abs(self) -> Self; Self::signum(self) -> Self; Self::is_sign_positive(self) -> bool; Self::is_sign_negative(self) -> bool; Self::min(self, other: Self) -> Self; Self::max(self, other: Self) -> Self; Self::recip(self) -> Self; Self::powi(self, n: i32) -> Self; Self::to_degrees(self) -> Self; Self::to_radians(self) -> Self; } } impl FloatCore for f64 { constant! { infinity() -> f64::INFINITY; neg_infinity() -> f64::NEG_INFINITY; nan() -> f64::NAN; neg_zero() -> -0.0; min_value() -> f64::MIN; min_positive_value() -> f64::MIN_POSITIVE; epsilon() -> f64::EPSILON; max_value() -> f64::MAX; } #[inline] fn integer_decode(self) -> (u64, i16, i8) { integer_decode_f64(self) } #[inline] #[cfg(not(feature = "std"))] fn classify(self) -> FpCategory { const EXP_MASK: u64 = 0x7ff0000000000000; const MAN_MASK: u64 = 0x000fffffffffffff; // Safety: this identical to the implementation of f64::to_bits(), // which is only available starting at Rust 1.20 let bits: u64 = unsafe { mem::transmute(self) }; match (bits & MAN_MASK, bits & EXP_MASK) { (0, 0) => FpCategory::Zero, (_, 0) => FpCategory::Subnormal, (0, EXP_MASK) => FpCategory::Infinite, (_, EXP_MASK) => FpCategory::Nan, _ => FpCategory::Normal, } } #[inline] #[cfg(not(feature = "std"))] fn to_degrees(self) -> Self { // The division here is correctly rounded with respect to the true // value of 180/π. (This differs from f32, where a constant must be // used to ensure a correctly rounded result.) self * (180.0 / f64::consts::PI) } #[inline] #[cfg(not(feature = "std"))] fn to_radians(self) -> Self { self * (f64::consts::PI / 180.0) } #[cfg(feature = "std")] forward! { Self::is_nan(self) -> bool; Self::is_infinite(self) -> bool; Self::is_finite(self) -> bool; Self::is_normal(self) -> bool; Self::classify(self) -> FpCategory; Self::floor(self) -> Self; Self::ceil(self) -> Self; Self::round(self) -> Self; Self::trunc(self) -> Self; Self::fract(self) -> Self; Self::abs(self) -> Self; Self::signum(self) -> Self; Self::is_sign_positive(self) -> bool; Self::is_sign_negative(self) -> bool; Self::min(self, other: Self) -> Self; Self::max(self, other: Self) -> Self; Self::recip(self) -> Self; Self::powi(self, n: i32) -> Self; Self::to_degrees(self) -> Self; Self::to_radians(self) -> Self; } } // FIXME: these doctests aren't actually helpful, because they're using and // testing the inherent methods directly, not going through `Float`. /// Generic trait for floating point numbers /// /// This trait is only available with the `std` feature, or with the `libm` feature otherwise. #[cfg(any(feature = "std", feature = "libm"))] pub trait Float: Num + Copy + NumCast + PartialOrd + Neg { /// Returns the `NaN` value. /// /// ``` /// use num_traits::Float; /// /// let nan: f32 = Float::nan(); /// /// assert!(nan.is_nan()); /// ``` fn nan() -> Self; /// Returns the infinite value. /// /// ``` /// use num_traits::Float; /// use std::f32; /// /// let infinity: f32 = Float::infinity(); /// /// assert!(infinity.is_infinite()); /// assert!(!infinity.is_finite()); /// assert!(infinity > f32::MAX); /// ``` fn infinity() -> Self; /// Returns the negative infinite value. /// /// ``` /// use num_traits::Float; /// use std::f32; /// /// let neg_infinity: f32 = Float::neg_infinity(); /// /// assert!(neg_infinity.is_infinite()); /// assert!(!neg_infinity.is_finite()); /// assert!(neg_infinity < f32::MIN); /// ``` fn neg_infinity() -> Self; /// Returns `-0.0`. /// /// ``` /// use num_traits::{Zero, Float}; /// /// let inf: f32 = Float::infinity(); /// let zero: f32 = Zero::zero(); /// let neg_zero: f32 = Float::neg_zero(); /// /// assert_eq!(zero, neg_zero); /// assert_eq!(7.0f32/inf, zero); /// assert_eq!(zero * 10.0, zero); /// ``` fn neg_zero() -> Self; /// Returns the smallest finite value that this type can represent. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let x: f64 = Float::min_value(); /// /// assert_eq!(x, f64::MIN); /// ``` fn min_value() -> Self; /// Returns the smallest positive, normalized value that this type can represent. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let x: f64 = Float::min_positive_value(); /// /// assert_eq!(x, f64::MIN_POSITIVE); /// ``` fn min_positive_value() -> Self; /// Returns epsilon, a small positive value. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let x: f64 = Float::epsilon(); /// /// assert_eq!(x, f64::EPSILON); /// ``` /// /// # Panics /// /// The default implementation will panic if `f32::EPSILON` cannot /// be cast to `Self`. fn epsilon() -> Self { Self::from(f32::EPSILON).expect("Unable to cast from f32::EPSILON") } /// Returns the largest finite value that this type can represent. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let x: f64 = Float::max_value(); /// assert_eq!(x, f64::MAX); /// ``` fn max_value() -> Self; /// Returns `true` if this value is `NaN` and false otherwise. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let nan = f64::NAN; /// let f = 7.0; /// /// assert!(nan.is_nan()); /// assert!(!f.is_nan()); /// ``` fn is_nan(self) -> bool; /// Returns `true` if this value is positive infinity or negative infinity and /// false otherwise. /// /// ``` /// use num_traits::Float; /// use std::f32; /// /// let f = 7.0f32; /// let inf: f32 = Float::infinity(); /// let neg_inf: f32 = Float::neg_infinity(); /// let nan: f32 = f32::NAN; /// /// assert!(!f.is_infinite()); /// assert!(!nan.is_infinite()); /// /// assert!(inf.is_infinite()); /// assert!(neg_inf.is_infinite()); /// ``` fn is_infinite(self) -> bool; /// Returns `true` if this number is neither infinite nor `NaN`. /// /// ``` /// use num_traits::Float; /// use std::f32; /// /// let f = 7.0f32; /// let inf: f32 = Float::infinity(); /// let neg_inf: f32 = Float::neg_infinity(); /// let nan: f32 = f32::NAN; /// /// assert!(f.is_finite()); /// /// assert!(!nan.is_finite()); /// assert!(!inf.is_finite()); /// assert!(!neg_inf.is_finite()); /// ``` fn is_finite(self) -> bool; /// Returns `true` if the number is neither zero, infinite, /// [subnormal][subnormal], or `NaN`. /// /// ``` /// use num_traits::Float; /// use std::f32; /// /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32 /// let max = f32::MAX; /// let lower_than_min = 1.0e-40_f32; /// let zero = 0.0f32; /// /// assert!(min.is_normal()); /// assert!(max.is_normal()); /// /// assert!(!zero.is_normal()); /// assert!(!f32::NAN.is_normal()); /// assert!(!f32::INFINITY.is_normal()); /// // Values between `0` and `min` are Subnormal. /// assert!(!lower_than_min.is_normal()); /// ``` /// [subnormal]: http://en.wikipedia.org/wiki/Denormal_number fn is_normal(self) -> bool; /// Returns the floating point category of the number. If only one property /// is going to be tested, it is generally faster to use the specific /// predicate instead. /// /// ``` /// use num_traits::Float; /// use std::num::FpCategory; /// use std::f32; /// /// let num = 12.4f32; /// let inf = f32::INFINITY; /// /// assert_eq!(num.classify(), FpCategory::Normal); /// assert_eq!(inf.classify(), FpCategory::Infinite); /// ``` fn classify(self) -> FpCategory; /// Returns the largest integer less than or equal to a number. /// /// ``` /// use num_traits::Float; /// /// let f = 3.99; /// let g = 3.0; /// /// assert_eq!(f.floor(), 3.0); /// assert_eq!(g.floor(), 3.0); /// ``` fn floor(self) -> Self; /// Returns the smallest integer greater than or equal to a number. /// /// ``` /// use num_traits::Float; /// /// let f = 3.01; /// let g = 4.0; /// /// assert_eq!(f.ceil(), 4.0); /// assert_eq!(g.ceil(), 4.0); /// ``` fn ceil(self) -> Self; /// Returns the nearest integer to a number. Round half-way cases away from /// `0.0`. /// /// ``` /// use num_traits::Float; /// /// let f = 3.3; /// let g = -3.3; /// /// assert_eq!(f.round(), 3.0); /// assert_eq!(g.round(), -3.0); /// ``` fn round(self) -> Self; /// Return the integer part of a number. /// /// ``` /// use num_traits::Float; /// /// let f = 3.3; /// let g = -3.7; /// /// assert_eq!(f.trunc(), 3.0); /// assert_eq!(g.trunc(), -3.0); /// ``` fn trunc(self) -> Self; /// Returns the fractional part of a number. /// /// ``` /// use num_traits::Float; /// /// let x = 3.5; /// let y = -3.5; /// let abs_difference_x = (x.fract() - 0.5).abs(); /// let abs_difference_y = (y.fract() - (-0.5)).abs(); /// /// assert!(abs_difference_x < 1e-10); /// assert!(abs_difference_y < 1e-10); /// ``` fn fract(self) -> Self; /// Computes the absolute value of `self`. Returns `Float::nan()` if the /// number is `Float::nan()`. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let x = 3.5; /// let y = -3.5; /// /// let abs_difference_x = (x.abs() - x).abs(); /// let abs_difference_y = (y.abs() - (-y)).abs(); /// /// assert!(abs_difference_x < 1e-10); /// assert!(abs_difference_y < 1e-10); /// /// assert!(f64::NAN.abs().is_nan()); /// ``` fn abs(self) -> Self; /// Returns a number that represents the sign of `self`. /// /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()` /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()` /// - `Float::nan()` if the number is `Float::nan()` /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let f = 3.5; /// /// assert_eq!(f.signum(), 1.0); /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0); /// /// assert!(f64::NAN.signum().is_nan()); /// ``` fn signum(self) -> Self; /// Returns `true` if `self` is positive, including `+0.0`, /// `Float::infinity()`, and since Rust 1.20 also `Float::nan()`. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let neg_nan: f64 = -f64::NAN; /// /// let f = 7.0; /// let g = -7.0; /// /// assert!(f.is_sign_positive()); /// assert!(!g.is_sign_positive()); /// assert!(!neg_nan.is_sign_positive()); /// ``` fn is_sign_positive(self) -> bool; /// Returns `true` if `self` is negative, including `-0.0`, /// `Float::neg_infinity()`, and since Rust 1.20 also `-Float::nan()`. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let nan: f64 = f64::NAN; /// /// let f = 7.0; /// let g = -7.0; /// /// assert!(!f.is_sign_negative()); /// assert!(g.is_sign_negative()); /// assert!(!nan.is_sign_negative()); /// ``` fn is_sign_negative(self) -> bool; /// Fused multiply-add. Computes `(self * a) + b` with only one rounding /// error, yielding a more accurate result than an unfused multiply-add. /// /// Using `mul_add` can be more performant than an unfused multiply-add if /// the target architecture has a dedicated `fma` CPU instruction. /// /// ``` /// use num_traits::Float; /// /// let m = 10.0; /// let x = 4.0; /// let b = 60.0; /// /// // 100.0 /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn mul_add(self, a: Self, b: Self) -> Self; /// Take the reciprocal (inverse) of a number, `1/x`. /// /// ``` /// use num_traits::Float; /// /// let x = 2.0; /// let abs_difference = (x.recip() - (1.0/x)).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn recip(self) -> Self; /// Raise a number to an integer power. /// /// Using this function is generally faster than using `powf` /// /// ``` /// use num_traits::Float; /// /// let x = 2.0; /// let abs_difference = (x.powi(2) - x*x).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn powi(self, n: i32) -> Self; /// Raise a number to a floating point power. /// /// ``` /// use num_traits::Float; /// /// let x = 2.0; /// let abs_difference = (x.powf(2.0) - x*x).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn powf(self, n: Self) -> Self; /// Take the square root of a number. /// /// Returns NaN if `self` is a negative number. /// /// ``` /// use num_traits::Float; /// /// let positive = 4.0; /// let negative = -4.0; /// /// let abs_difference = (positive.sqrt() - 2.0).abs(); /// /// assert!(abs_difference < 1e-10); /// assert!(negative.sqrt().is_nan()); /// ``` fn sqrt(self) -> Self; /// Returns `e^(self)`, (the exponential function). /// /// ``` /// use num_traits::Float; /// /// let one = 1.0; /// // e^1 /// let e = one.exp(); /// /// // ln(e) - 1 == 0 /// let abs_difference = (e.ln() - 1.0).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn exp(self) -> Self; /// Returns `2^(self)`. /// /// ``` /// use num_traits::Float; /// /// let f = 2.0; /// /// // 2^2 - 4 == 0 /// let abs_difference = (f.exp2() - 4.0).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn exp2(self) -> Self; /// Returns the natural logarithm of the number. /// /// ``` /// use num_traits::Float; /// /// let one = 1.0; /// // e^1 /// let e = one.exp(); /// /// // ln(e) - 1 == 0 /// let abs_difference = (e.ln() - 1.0).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn ln(self) -> Self; /// Returns the logarithm of the number with respect to an arbitrary base. /// /// ``` /// use num_traits::Float; /// /// let ten = 10.0; /// let two = 2.0; /// /// // log10(10) - 1 == 0 /// let abs_difference_10 = (ten.log(10.0) - 1.0).abs(); /// /// // log2(2) - 1 == 0 /// let abs_difference_2 = (two.log(2.0) - 1.0).abs(); /// /// assert!(abs_difference_10 < 1e-10); /// assert!(abs_difference_2 < 1e-10); /// ``` fn log(self, base: Self) -> Self; /// Returns the base 2 logarithm of the number. /// /// ``` /// use num_traits::Float; /// /// let two = 2.0; /// /// // log2(2) - 1 == 0 /// let abs_difference = (two.log2() - 1.0).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn log2(self) -> Self; /// Returns the base 10 logarithm of the number. /// /// ``` /// use num_traits::Float; /// /// let ten = 10.0; /// /// // log10(10) - 1 == 0 /// let abs_difference = (ten.log10() - 1.0).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn log10(self) -> Self; /// Converts radians to degrees. /// /// ``` /// use std::f64::consts; /// /// let angle = consts::PI; /// /// let abs_difference = (angle.to_degrees() - 180.0).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` #[inline] fn to_degrees(self) -> Self { let halfpi = Self::zero().acos(); let ninety = Self::from(90u8).unwrap(); self * ninety / halfpi } /// Converts degrees to radians. /// /// ``` /// use std::f64::consts; /// /// let angle = 180.0_f64; /// /// let abs_difference = (angle.to_radians() - consts::PI).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` #[inline] fn to_radians(self) -> Self { let halfpi = Self::zero().acos(); let ninety = Self::from(90u8).unwrap(); self * halfpi / ninety } /// Returns the maximum of the two numbers. /// /// ``` /// use num_traits::Float; /// /// let x = 1.0; /// let y = 2.0; /// /// assert_eq!(x.max(y), y); /// ``` fn max(self, other: Self) -> Self; /// Returns the minimum of the two numbers. /// /// ``` /// use num_traits::Float; /// /// let x = 1.0; /// let y = 2.0; /// /// assert_eq!(x.min(y), x); /// ``` fn min(self, other: Self) -> Self; /// The positive difference of two numbers. /// /// * If `self <= other`: `0:0` /// * Else: `self - other` /// /// ``` /// use num_traits::Float; /// /// let x = 3.0; /// let y = -3.0; /// /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs(); /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs(); /// /// assert!(abs_difference_x < 1e-10); /// assert!(abs_difference_y < 1e-10); /// ``` fn abs_sub(self, other: Self) -> Self; /// Take the cubic root of a number. /// /// ``` /// use num_traits::Float; /// /// let x = 8.0; /// /// // x^(1/3) - 2 == 0 /// let abs_difference = (x.cbrt() - 2.0).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn cbrt(self) -> Self; /// Calculate the length of the hypotenuse of a right-angle triangle given /// legs of length `x` and `y`. /// /// ``` /// use num_traits::Float; /// /// let x = 2.0; /// let y = 3.0; /// /// // sqrt(x^2 + y^2) /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn hypot(self, other: Self) -> Self; /// Computes the sine of a number (in radians). /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let x = f64::consts::PI/2.0; /// /// let abs_difference = (x.sin() - 1.0).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn sin(self) -> Self; /// Computes the cosine of a number (in radians). /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let x = 2.0*f64::consts::PI; /// /// let abs_difference = (x.cos() - 1.0).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn cos(self) -> Self; /// Computes the tangent of a number (in radians). /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let x = f64::consts::PI/4.0; /// let abs_difference = (x.tan() - 1.0).abs(); /// /// assert!(abs_difference < 1e-14); /// ``` fn tan(self) -> Self; /// Computes the arcsine of a number. Return value is in radians in /// the range [-pi/2, pi/2] or NaN if the number is outside the range /// [-1, 1]. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let f = f64::consts::PI / 2.0; /// /// // asin(sin(pi/2)) /// let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn asin(self) -> Self; /// Computes the arccosine of a number. Return value is in radians in /// the range [0, pi] or NaN if the number is outside the range /// [-1, 1]. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let f = f64::consts::PI / 4.0; /// /// // acos(cos(pi/4)) /// let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn acos(self) -> Self; /// Computes the arctangent of a number. Return value is in radians in the /// range [-pi/2, pi/2]; /// /// ``` /// use num_traits::Float; /// /// let f = 1.0; /// /// // atan(tan(1)) /// let abs_difference = (f.tan().atan() - 1.0).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn atan(self) -> Self; /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`). /// /// * `x = 0`, `y = 0`: `0` /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]` /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]` /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)` /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let pi = f64::consts::PI; /// // All angles from horizontal right (+x) /// // 45 deg counter-clockwise /// let x1 = 3.0; /// let y1 = -3.0; /// /// // 135 deg clockwise /// let x2 = -3.0; /// let y2 = 3.0; /// /// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs(); /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs(); /// /// assert!(abs_difference_1 < 1e-10); /// assert!(abs_difference_2 < 1e-10); /// ``` fn atan2(self, other: Self) -> Self; /// Simultaneously computes the sine and cosine of the number, `x`. Returns /// `(sin(x), cos(x))`. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let x = f64::consts::PI/4.0; /// let f = x.sin_cos(); /// /// let abs_difference_0 = (f.0 - x.sin()).abs(); /// let abs_difference_1 = (f.1 - x.cos()).abs(); /// /// assert!(abs_difference_0 < 1e-10); /// assert!(abs_difference_0 < 1e-10); /// ``` fn sin_cos(self) -> (Self, Self); /// Returns `e^(self) - 1` in a way that is accurate even if the /// number is close to zero. /// /// ``` /// use num_traits::Float; /// /// let x = 7.0; /// /// // e^(ln(7)) - 1 /// let abs_difference = (x.ln().exp_m1() - 6.0).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn exp_m1(self) -> Self; /// Returns `ln(1+n)` (natural logarithm) more accurately than if /// the operations were performed separately. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let x = f64::consts::E - 1.0; /// /// // ln(1 + (e - 1)) == ln(e) == 1 /// let abs_difference = (x.ln_1p() - 1.0).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn ln_1p(self) -> Self; /// Hyperbolic sine function. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let e = f64::consts::E; /// let x = 1.0; /// /// let f = x.sinh(); /// // Solving sinh() at 1 gives `(e^2-1)/(2e)` /// let g = (e*e - 1.0)/(2.0*e); /// let abs_difference = (f - g).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn sinh(self) -> Self; /// Hyperbolic cosine function. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let e = f64::consts::E; /// let x = 1.0; /// let f = x.cosh(); /// // Solving cosh() at 1 gives this result /// let g = (e*e + 1.0)/(2.0*e); /// let abs_difference = (f - g).abs(); /// /// // Same result /// assert!(abs_difference < 1.0e-10); /// ``` fn cosh(self) -> Self; /// Hyperbolic tangent function. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let e = f64::consts::E; /// let x = 1.0; /// /// let f = x.tanh(); /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))` /// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2)); /// let abs_difference = (f - g).abs(); /// /// assert!(abs_difference < 1.0e-10); /// ``` fn tanh(self) -> Self; /// Inverse hyperbolic sine function. /// /// ``` /// use num_traits::Float; /// /// let x = 1.0; /// let f = x.sinh().asinh(); /// /// let abs_difference = (f - x).abs(); /// /// assert!(abs_difference < 1.0e-10); /// ``` fn asinh(self) -> Self; /// Inverse hyperbolic cosine function. /// /// ``` /// use num_traits::Float; /// /// let x = 1.0; /// let f = x.cosh().acosh(); /// /// let abs_difference = (f - x).abs(); /// /// assert!(abs_difference < 1.0e-10); /// ``` fn acosh(self) -> Self; /// Inverse hyperbolic tangent function. /// /// ``` /// use num_traits::Float; /// use std::f64; /// /// let e = f64::consts::E; /// let f = e.tanh().atanh(); /// /// let abs_difference = (f - e).abs(); /// /// assert!(abs_difference < 1.0e-10); /// ``` fn atanh(self) -> Self; /// Returns the mantissa, base 2 exponent, and sign as integers, respectively. /// The original number can be recovered by `sign * mantissa * 2 ^ exponent`. /// /// ``` /// use num_traits::Float; /// /// let num = 2.0f32; /// /// // (8388608, -22, 1) /// let (mantissa, exponent, sign) = Float::integer_decode(num); /// let sign_f = sign as f32; /// let mantissa_f = mantissa as f32; /// let exponent_f = num.powf(exponent as f32); /// /// // 1 * 8388608 * 2^(-22) == 2 /// let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs(); /// /// assert!(abs_difference < 1e-10); /// ``` fn integer_decode(self) -> (u64, i16, i8); } #[cfg(feature = "std")] macro_rules! float_impl_std { ($T:ident $decode:ident) => { impl Float for $T { constant! { nan() -> $T::NAN; infinity() -> $T::INFINITY; neg_infinity() -> $T::NEG_INFINITY; neg_zero() -> -0.0; min_value() -> $T::MIN; min_positive_value() -> $T::MIN_POSITIVE; epsilon() -> $T::EPSILON; max_value() -> $T::MAX; } #[inline] #[allow(deprecated)] fn abs_sub(self, other: Self) -> Self { <$T>::abs_sub(self, other) } #[inline] fn integer_decode(self) -> (u64, i16, i8) { $decode(self) } forward! { Self::is_nan(self) -> bool; Self::is_infinite(self) -> bool; Self::is_finite(self) -> bool; Self::is_normal(self) -> bool; Self::classify(self) -> FpCategory; Self::floor(self) -> Self; Self::ceil(self) -> Self; Self::round(self) -> Self; Self::trunc(self) -> Self; Self::fract(self) -> Self; Self::abs(self) -> Self; Self::signum(self) -> Self; Self::is_sign_positive(self) -> bool; Self::is_sign_negative(self) -> bool; Self::mul_add(self, a: Self, b: Self) -> Self; Self::recip(self) -> Self; Self::powi(self, n: i32) -> Self; Self::powf(self, n: Self) -> Self; Self::sqrt(self) -> Self; Self::exp(self) -> Self; Self::exp2(self) -> Self; Self::ln(self) -> Self; Self::log(self, base: Self) -> Self; Self::log2(self) -> Self; Self::log10(self) -> Self; Self::to_degrees(self) -> Self; Self::to_radians(self) -> Self; Self::max(self, other: Self) -> Self; Self::min(self, other: Self) -> Self; Self::cbrt(self) -> Self; Self::hypot(self, other: Self) -> Self; Self::sin(self) -> Self; Self::cos(self) -> Self; Self::tan(self) -> Self; Self::asin(self) -> Self; Self::acos(self) -> Self; Self::atan(self) -> Self; Self::atan2(self, other: Self) -> Self; Self::sin_cos(self) -> (Self, Self); Self::exp_m1(self) -> Self; Self::ln_1p(self) -> Self; Self::sinh(self) -> Self; Self::cosh(self) -> Self; Self::tanh(self) -> Self; Self::asinh(self) -> Self; Self::acosh(self) -> Self; Self::atanh(self) -> Self; } } }; } #[cfg(all(not(feature = "std"), feature = "libm"))] macro_rules! float_impl_libm { ($T:ident $decode:ident) => { constant! { nan() -> $T::NAN; infinity() -> $T::INFINITY; neg_infinity() -> $T::NEG_INFINITY; neg_zero() -> -0.0; min_value() -> $T::MIN; min_positive_value() -> $T::MIN_POSITIVE; epsilon() -> $T::EPSILON; max_value() -> $T::MAX; } #[inline] fn integer_decode(self) -> (u64, i16, i8) { $decode(self) } #[inline] fn fract(self) -> Self { self - FloatCore::trunc(self) } #[inline] fn log(self, base: Self) -> Self { self.ln() / base.ln() } forward! { FloatCore::is_nan(self) -> bool; FloatCore::is_infinite(self) -> bool; FloatCore::is_finite(self) -> bool; FloatCore::is_normal(self) -> bool; FloatCore::classify(self) -> FpCategory; FloatCore::signum(self) -> Self; FloatCore::is_sign_positive(self) -> bool; FloatCore::is_sign_negative(self) -> bool; FloatCore::recip(self) -> Self; FloatCore::powi(self, n: i32) -> Self; FloatCore::to_degrees(self) -> Self; FloatCore::to_radians(self) -> Self; FloatCore::max(self, other: Self) -> Self; FloatCore::min(self, other: Self) -> Self; } }; } fn integer_decode_f32(f: f32) -> (u64, i16, i8) { // Safety: this identical to the implementation of f32::to_bits(), // which is only available starting at Rust 1.20 let bits: u32 = unsafe { mem::transmute(f) }; let sign: i8 = if bits >> 31 == 0 { 1 } else { -1 }; let mut exponent: i16 = ((bits >> 23) & 0xff) as i16; let mantissa = if exponent == 0 { (bits & 0x7fffff) << 1 } else { (bits & 0x7fffff) | 0x800000 }; // Exponent bias + mantissa shift exponent -= 127 + 23; (mantissa as u64, exponent, sign) } fn integer_decode_f64(f: f64) -> (u64, i16, i8) { // Safety: this identical to the implementation of f64::to_bits(), // which is only available starting at Rust 1.20 let bits: u64 = unsafe { mem::transmute(f) }; let sign: i8 = if bits >> 63 == 0 { 1 } else { -1 }; let mut exponent: i16 = ((bits >> 52) & 0x7ff) as i16; let mantissa = if exponent == 0 { (bits & 0xfffffffffffff) << 1 } else { (bits & 0xfffffffffffff) | 0x10000000000000 }; // Exponent bias + mantissa shift exponent -= 1023 + 52; (mantissa, exponent, sign) } #[cfg(feature = "std")] float_impl_std!(f32 integer_decode_f32); #[cfg(feature = "std")] float_impl_std!(f64 integer_decode_f64); #[cfg(all(not(feature = "std"), feature = "libm"))] impl Float for f32 { float_impl_libm!(f32 integer_decode_f32); #[inline] #[allow(deprecated)] fn abs_sub(self, other: Self) -> Self { libm::fdimf(self, other) } #[inline] fn floor(self) -> Self { libm::floorf(self) } #[inline] fn ceil(self) -> Self { libm::ceilf(self) } #[inline] fn round(self) -> Self { libm::roundf(self) } #[inline] fn trunc(self) -> Self { libm::truncf(self) } #[inline] fn abs(self) -> Self { libm::fabsf(self) } #[inline] fn mul_add(self, a: Self, b: Self) -> Self { libm::fmaf(self, a, b) } #[inline] fn powf(self, n: Self) -> Self { libm::powf(self, n) } #[inline] fn sqrt(self) -> Self { libm::sqrtf(self) } #[inline] fn exp(self) -> Self { libm::expf(self) } #[inline] fn exp2(self) -> Self { libm::exp2f(self) } #[inline] fn ln(self) -> Self { libm::logf(self) } #[inline] fn log2(self) -> Self { libm::log2f(self) } #[inline] fn log10(self) -> Self { libm::log10f(self) } #[inline] fn cbrt(self) -> Self { libm::cbrtf(self) } #[inline] fn hypot(self, other: Self) -> Self { libm::hypotf(self, other) } #[inline] fn sin(self) -> Self { libm::sinf(self) } #[inline] fn cos(self) -> Self { libm::cosf(self) } #[inline] fn tan(self) -> Self { libm::tanf(self) } #[inline] fn asin(self) -> Self { libm::asinf(self) } #[inline] fn acos(self) -> Self { libm::acosf(self) } #[inline] fn atan(self) -> Self { libm::atanf(self) } #[inline] fn atan2(self, other: Self) -> Self { libm::atan2f(self, other) } #[inline] fn sin_cos(self) -> (Self, Self) { libm::sincosf(self) } #[inline] fn exp_m1(self) -> Self { libm::expm1f(self) } #[inline] fn ln_1p(self) -> Self { libm::log1pf(self) } #[inline] fn sinh(self) -> Self { libm::sinhf(self) } #[inline] fn cosh(self) -> Self { libm::coshf(self) } #[inline] fn tanh(self) -> Self { libm::tanhf(self) } #[inline] fn asinh(self) -> Self { libm::asinhf(self) } #[inline] fn acosh(self) -> Self { libm::acoshf(self) } #[inline] fn atanh(self) -> Self { libm::atanhf(self) } } #[cfg(all(not(feature = "std"), feature = "libm"))] impl Float for f64 { float_impl_libm!(f64 integer_decode_f64); #[inline] #[allow(deprecated)] fn abs_sub(self, other: Self) -> Self { libm::fdim(self, other) } #[inline] fn floor(self) -> Self { libm::floor(self) } #[inline] fn ceil(self) -> Self { libm::ceil(self) } #[inline] fn round(self) -> Self { libm::round(self) } #[inline] fn trunc(self) -> Self { libm::trunc(self) } #[inline] fn abs(self) -> Self { libm::fabs(self) } #[inline] fn mul_add(self, a: Self, b: Self) -> Self { libm::fma(self, a, b) } #[inline] fn powf(self, n: Self) -> Self { libm::pow(self, n) } #[inline] fn sqrt(self) -> Self { libm::sqrt(self) } #[inline] fn exp(self) -> Self { libm::exp(self) } #[inline] fn exp2(self) -> Self { libm::exp2(self) } #[inline] fn ln(self) -> Self { libm::log(self) } #[inline] fn log2(self) -> Self { libm::log2(self) } #[inline] fn log10(self) -> Self { libm::log10(self) } #[inline] fn cbrt(self) -> Self { libm::cbrt(self) } #[inline] fn hypot(self, other: Self) -> Self { libm::hypot(self, other) } #[inline] fn sin(self) -> Self { libm::sin(self) } #[inline] fn cos(self) -> Self { libm::cos(self) } #[inline] fn tan(self) -> Self { libm::tan(self) } #[inline] fn asin(self) -> Self { libm::asin(self) } #[inline] fn acos(self) -> Self { libm::acos(self) } #[inline] fn atan(self) -> Self { libm::atan(self) } #[inline] fn atan2(self, other: Self) -> Self { libm::atan2(self, other) } #[inline] fn sin_cos(self) -> (Self, Self) { libm::sincos(self) } #[inline] fn exp_m1(self) -> Self { libm::expm1(self) } #[inline] fn ln_1p(self) -> Self { libm::log1p(self) } #[inline] fn sinh(self) -> Self { libm::sinh(self) } #[inline] fn cosh(self) -> Self { libm::cosh(self) } #[inline] fn tanh(self) -> Self { libm::tanh(self) } #[inline] fn asinh(self) -> Self { libm::asinh(self) } #[inline] fn acosh(self) -> Self { libm::acosh(self) } #[inline] fn atanh(self) -> Self { libm::atanh(self) } } macro_rules! float_const_impl { ($(#[$doc:meta] $constant:ident,)+) => ( #[allow(non_snake_case)] pub trait FloatConst { $(#[$doc] fn $constant() -> Self;)+ #[doc = "Return the full circle constant `τ`."] #[inline] fn TAU() -> Self where Self: Sized + Add { Self::PI() + Self::PI() } #[doc = "Return `log10(2.0)`."] #[inline] fn LOG10_2() -> Self where Self: Sized + Div { Self::LN_2() / Self::LN_10() } #[doc = "Return `log2(10.0)`."] #[inline] fn LOG2_10() -> Self where Self: Sized + Div { Self::LN_10() / Self::LN_2() } } float_const_impl! { @float f32, $($constant,)+ } float_const_impl! { @float f64, $($constant,)+ } ); (@float $T:ident, $($constant:ident,)+) => ( impl FloatConst for $T { constant! { $( $constant() -> $T::consts::$constant; )+ TAU() -> 6.28318530717958647692528676655900577; LOG10_2() -> 0.301029995663981195213738894724493027; LOG2_10() -> 3.32192809488736234787031942948939018; } } ); } float_const_impl! { #[doc = "Return Euler’s number."] E, #[doc = "Return `1.0 / π`."] FRAC_1_PI, #[doc = "Return `1.0 / sqrt(2.0)`."] FRAC_1_SQRT_2, #[doc = "Return `2.0 / π`."] FRAC_2_PI, #[doc = "Return `2.0 / sqrt(π)`."] FRAC_2_SQRT_PI, #[doc = "Return `π / 2.0`."] FRAC_PI_2, #[doc = "Return `π / 3.0`."] FRAC_PI_3, #[doc = "Return `π / 4.0`."] FRAC_PI_4, #[doc = "Return `π / 6.0`."] FRAC_PI_6, #[doc = "Return `π / 8.0`."] FRAC_PI_8, #[doc = "Return `ln(10.0)`."] LN_10, #[doc = "Return `ln(2.0)`."] LN_2, #[doc = "Return `log10(e)`."] LOG10_E, #[doc = "Return `log2(e)`."] LOG2_E, #[doc = "Return Archimedes’ constant `π`."] PI, #[doc = "Return `sqrt(2.0)`."] SQRT_2, } #[cfg(test)] mod tests { use core::f64::consts; const DEG_RAD_PAIRS: [(f64, f64); 7] = [ (0.0, 0.), (22.5, consts::FRAC_PI_8), (30.0, consts::FRAC_PI_6), (45.0, consts::FRAC_PI_4), (60.0, consts::FRAC_PI_3), (90.0, consts::FRAC_PI_2), (180.0, consts::PI), ]; #[test] fn convert_deg_rad() { use float::FloatCore; for &(deg, rad) in &DEG_RAD_PAIRS { assert!((FloatCore::to_degrees(rad) - deg).abs() < 1e-6); assert!((FloatCore::to_radians(deg) - rad).abs() < 1e-6); let (deg, rad) = (deg as f32, rad as f32); assert!((FloatCore::to_degrees(rad) - deg).abs() < 1e-5); assert!((FloatCore::to_radians(deg) - rad).abs() < 1e-5); } } #[cfg(any(feature = "std", feature = "libm"))] #[test] fn convert_deg_rad_std() { for &(deg, rad) in &DEG_RAD_PAIRS { use Float; assert!((Float::to_degrees(rad) - deg).abs() < 1e-6); assert!((Float::to_radians(deg) - rad).abs() < 1e-6); let (deg, rad) = (deg as f32, rad as f32); assert!((Float::to_degrees(rad) - deg).abs() < 1e-5); assert!((Float::to_radians(deg) - rad).abs() < 1e-5); } } #[test] // This fails with the forwarded `std` implementation in Rust 1.8. // To avoid the failure, the test is limited to `no_std` builds. #[cfg(not(feature = "std"))] fn to_degrees_rounding() { use float::FloatCore; assert_eq!( FloatCore::to_degrees(1_f32), 57.2957795130823208767981548141051703 ); } #[test] #[cfg(any(feature = "std", feature = "libm"))] fn extra_logs() { use float::{Float, FloatConst}; fn check(diff: F) { let _2 = F::from(2.0).unwrap(); assert!((F::LOG10_2() - F::log10(_2)).abs() < diff); assert!((F::LOG10_2() - F::LN_2() / F::LN_10()).abs() < diff); let _10 = F::from(10.0).unwrap(); assert!((F::LOG2_10() - F::log2(_10)).abs() < diff); assert!((F::LOG2_10() - F::LN_10() / F::LN_2()).abs() < diff); } check::(1e-6); check::(1e-12); } }